Solve for $f$. $2+1.25f=10-2.75f$ $f=$
Solution: We need to manipulate the equation to get $ f $ by itself. $\begin{aligned} 2+1.25f&=10-2.75f \\\\ 2+1.25f {+2.75f} &= 10-2.75f{+2.75f} &&\gray{\text{Add 2.75f to each side.}}\\\\ 4f+2&=10 &&\gray{\text{Combine like terms.}}\\\\ 4f+2{-2} &= 10{-2} &&\gray{\text{Subtract 2 from each side.}}\\\\ 4f &=8 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{4f}{{4}} &= \dfrac{8}{{4}} &&\gray{\text{Divide each side by 4.}}\\\\ f &= {2} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $f = { 2 }~~~~~~~~$ [Let's check our work!]